Question:
$\phi=\int_{0}^{R}\int_{0}^{e_{f}}\varphi\epsilon_{f}d\epsilon_{f}\frac{2\pi~ r.dr}{Y_{y}}$ is related to}
$\phi=\int_{0}^{R}\int_{0}^{e_{f}}\varphi\epsilon_{f}d\epsilon_{f}\frac{2\pi~ r.dr}{Y_{y}}$ is related to}
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Fibre migration improves yarn cohesion and reduces weak points in yarn structure.
Updated On: Jul 4, 2026
- Fabric strength
- Fibre Migration
- Closed fibre spacing
- Castigliano's theorem
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The Correct Option is B
Solution and Explanation
Concept:
Fibre migration refers to the movement of fibres within the yarn cross-section during spinning and twisting processes. Fibres do not remain fixed at a single radial position; instead, they continuously migrate between core and surface regions, improving yarn uniformity and structural stability.
Step 1: Interpret mathematical expression.
The given double integral represents distribution of fibre strain energy across:
• radial position \(r\)
• strain level \(\epsilon_f\) This indicates variation of fibre behavior within yarn structure.
Step 2: Understand physical meaning.
Such integrals are used in modelling:
• fibre displacement
• internal stress distribution
• migration paths of fibres
Step 3: Link to concept.
Since the expression describes fibre movement and redistribution within yarn cross-section, it corresponds to fibre migration.
Step 4: Final conclusion.
\[ \boxed{\text{Fibre Migration}} \] Thus, \[ \boxed{\text{Option (B) is correct.}} \]
Step 1: Interpret mathematical expression.
The given double integral represents distribution of fibre strain energy across:
• radial position \(r\)
• strain level \(\epsilon_f\) This indicates variation of fibre behavior within yarn structure.
Step 2: Understand physical meaning.
Such integrals are used in modelling:
• fibre displacement
• internal stress distribution
• migration paths of fibres
Step 3: Link to concept.
Since the expression describes fibre movement and redistribution within yarn cross-section, it corresponds to fibre migration.
Step 4: Final conclusion.
\[ \boxed{\text{Fibre Migration}} \] Thus, \[ \boxed{\text{Option (B) is correct.}} \]
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